Omega open sets in generalized topological spaces

We extend the notion of omega open set in ordinary topological spaces to generalized topological spaces. We obtain several characterizations of omega open sets in generalized topological spaces and prove that they form a generalized topology. Using omega open sets we introduce characterizations of Lindelöf, compact, and countably compact concepts generalized topological spaces. Also, we generalize the concepts of continuity in generalized topological spaces via omega open sets.